# Ensemble Kalman Methods With Constraints

## TL;DR

This paper develops a general framework for incorporating equality and inequality constraints into Ensemble Kalman methods, enhancing their applicability in state and parameter estimation problems with prior information.

## Contribution

It introduces a novel methodology and theoretical justification for constrained Ensemble Kalman methods, supported by numerical experiments.

## Key findings

- Effective enforcement of constraints in Ensemble Kalman methods
- Theoretical validation of the constrained methodology
- Numerical experiments demonstrating improved estimation accuracy

## Abstract

Ensemble Kalman methods constitute an increasingly important tool in both state and parameter estimation problems. Their popularity stems from the derivative-free nature of the methodology which may be readily applied when computer code is available for the underlying state-space dynamics (for state estimation) or for the parameter-to-observable map (for parameter estimation). There are many applications in which it is desirable to enforce prior information in the form of equality or inequality constraints on the state or parameter. This paper establishes a general framework for doing so, describing a widely applicable methodology, a theory which justifies the methodology, and a set of numerical experiments exemplifying it.